In response to requests for collision safety and weight reduction, the tensile strength of a steel sheet applied to the body of an automobile or the like has exceeded 590 MPa class, and is now reaching as high as units of GPa. High-strength steel sheets can be provided with increased energy absorption at the time of a collision, increased strength, and the like without increasing sheet thickness. As compared to other light-weight materials, processing of parts, assembly, or the like using high-strength steel sheets do not always require large renovation of equipment and production technology. Therefore, loads of processing of parts, assembly, or the like using high-strength steel sheets on production costs are considered to be relatively small as compared to other light-weight materials.
However, in the case of press forming, springback, wrinkle, and the like increase along with increase in strength of steel sheets, and it becomes difficult to ensure dimensional accuracy of parts. Further, decrease in ductility accompanying increase in strength increases the risk of breakage during press forming. Realizing both performance and productivity with high-strength steel sheets is thus not always easy compared to conventional mild steel sheets.
Of the breakage, wrinkle, and springback described above, breakage and wrinkle are problems that may occur also where conventional mild steel sheets are used depending on the part shape, the forming conditions, and so on, and a multitude of knowledge, counter technology, and the like have been accumulated hitherto. On the other hand, the springback is a problem unique to the case where a high-strength steel sheet is used, for which sufficient studies are not conducted, and it cannot be said that those widely used forming simulations have achieved sufficient practical reliability for dimensional accuracy prediction by springback analysis.
Springback is elastic deformation which occurs in a part to satisfy a new balance with a residual stress being a driving force when an operation which alleviates a constraint on the part is performed, such as an operation to remove a formed product from a die after press forming or an operation to trim an unnecessary portion. The springback is large on the high-strength steel sheets, and hence it is difficult to ensure dimensional accuracy required in a final product.
The springback is categorized into “angular variation,” “wall warping,” “twisting (strain),” “edge line warping (surface warping),” and “springback of punch bottom” depending on phenomenon. All of them occur as a result of that a residual stress distribution operates in a part as the moment of bending or twisting, and the part deforms according to rigidity determined by elastic coefficient, sheet thickness, part shape, and so on of the material. For example, most well-known springback examples are bending angle variation, wall warping, and the like. For these springbacks, the stress distribution in a sheet thickness direction becomes a driving force, and the rigidity is determined mainly by the sheet thickness. On the other hand, when a beam of a hat cross section curving in a longitudinal direction is draw formed, wall warping and twisting occur, but when curvature of bending is small, part rigidity increases and the wall warping becomes small.
Based on this mechanism, one countermeasure method of dimensional accuracy defect is to change the sheet thickness, the part shape, and/or the like to increase the rigidity corresponding to an elastic deformation mode of springback, thereby increasing resistance to the springback.
Increase in resistance to springback surely decreases dimensional variations. The resistance to springback is the rigidity of a part with respect to the elastic deformation mode thereof. To increase the rigidity of a part, the shape of the part is an important factor. The shape of the part is restricted by requirements such as performance, layout, and so on, and hence small countermeasures such as beads, embossment, and the like are effective.
Beads with respect to wall warping are a most typical rigidity enforcement countermeasure example. On the other hand, it is difficult to find an optimal rigidity reinforcing position with respect to three-dimensional springback in a complicated part. As a new attempt, there has been proposed a method to use natural vibration analysis and optimization together. See Shunji Hiwatashi et al., “Comprehensive Effort For Forming Problems of High-Strength Steel Sheets,” Sheet Forming Forum Special Lecture, Formation and Quality Improvement Engineering Division (Sokei Sositsu Kogaku Bukai), The Iron and Steel Institute of Japan (Jan. 14, 2005).
Specifically, focusing attention on that a natural frequency is proportional to the square root of rigidity and is inversely proportional to the square root of density (mass), the elastic deformation mode of springback is identified, the natural vibration deformation mode corresponding to this elastic deformation mode of springback is selected, a part of elements is replaced with a highly elastic material of the same density so that the natural frequency of the natural vibration deformation mode increases, and an optimal disposition of these elements is obtained by using an optimizing tool or the like. It is thus possible to easily find an optimal rigidity reinforcement position.
However, with this method, it is necessary to manually and laboriously select the natural vibration deformation mode. Further, even if the natural vibration deformation mode is selected automatically, the criteria for selection are not clear. Thus, it is not always possible to select the natural vibration deformation mode corresponding to the elastic deformation mode of springback, and it is not always possible to obtain an optimal disposition of highly elastic materials. Accordingly, it is conceivable to select all natural vibration deformation modes and obtain the optimal disposition of highly elastic materials for each mode, but there is a problem that it would cost too much. Thus, it has not been possible to easily perform an analysis for reducing deformation of a member caused by springback.